Question

how many solutions are there for the pair of linear equation x=0 and x=2​

Answer 1

The pair of equations will be:

1. 1x + 0y + 0 = 0
2. 1x + 0y - 2 = 0

As  $\frac{b_{1} }{b_{2} } =$ not defined, and $\frac{a_{1} }{a_{2} } \neq \frac{c_{1} }{c_{2} }$,

the pair of equations is inconsistent.

Answer: No solution.

Answer 2

There are no solutions for the pair of linear equations $x=0$ and $x=2$.

Given,

A pair of linear equations: $x=0$ and $x=2$.

To Find,

The number of solutions for the given pair of linear equations.

Solution,

The method of finding the number of solutions for the pair of linear equations is as follows -

We know that every linear equation can be represented as a straight line in the XY plane.

We also know that the standard slope-intercept representation of a straight line is $y=mx+c$, where y and x are the Y and X coordinates respectively, m is the 'slope' and c is the 'y-intercept' of the straight line.

Now we will represent the given linear equations in the slope-intercept representation.

$x=0$  ⇒  $0.y=1.x+0$, so the slope of this straight line is 1.

$x=2$  ⇒  $x-2=0.y$  ⇒  $0.y=1.x-2$, so the slope of this line is also 1.

Since the slope of these two lines is the same, the two lines are parallel to each other. So these lines never intersect each other. This is why there is no solution for the pair of linear equations.

Hence, there are no solutions for the pair of linear equations $x=0$ and $x=2$.

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